Question

write the rules of each transformation. label the pre - image and image.

Explanation:

Step1: Identify pre - image and image

For the left figure, dashed is pre - image, solid is image. For right figure, solid is pre - image, dashed is image.

Step2: Analyze possible transformations

For left, could be translation. For right, could be rotation, reflection or dilation.

Step3: Determine transformation rules

For translation, find coordinate changes. For other transformations, find relevant elements like center of rotation/dilation or line of reflection.

Answer:

Without specific coordinates or clear - cut details about the nature of the transformation (translation, rotation, reflection, dilation), a full - fledged answer cannot be provided. However, in general terms:
For the left - hand side transformation of the octagon:
Let the pre - image be the dashed octagon and the image be the solid octagon. If we assume a translation, we need to find the change in the x and y coordinates of a corresponding vertex. For example, if a vertex of the pre - image has coordinates \((x_1,y_1)\) and the corresponding vertex of the image has coordinates \((x_2,y_2)\), the translation rule would be \((x,y)\to(x+(x_2 - x_1),y+(y_2 - y_1))\).
For the right - hand side transformation of the triangle:
Let the pre - image be the solid triangle and the image be the dashed triangle. If it is a rotation, we need to determine the center of rotation, the angle of rotation, and the direction (clockwise or counter - clockwise). If it is a reflection, we need to find the line of reflection. If it is a dilation, we need to find the center of dilation and the scale factor.